Simplify the following expression: $t = \dfrac{-2z^2 + 16z - 14}{z - 7} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ t =\dfrac{-2(z^2 - 8z + 7)}{z - 7} $ Then we factor the remaining polynomial: $z^2 {-8}z + {7} $ ${-7} {-1} = {-8}$ ${-7} \times {-1} = {7}$ $ (z {-7}) (z {-1}) $ This gives us a factored expression: $\dfrac{-2(z {-7}) (z {-1})}{z - 7}$ We can divide the numerator and denominator by $(z + 7)$ on condition that $z \neq 7$ Therefore $t = -2(z - 1); z \neq 7$